1. Field of the Invention
This invention relates in general to interferometric techniques for surface characterization. In particular, it relates to a new approach for measuring the height profile of a sample having an optically non-homogeneous surface resulting from a composite multi-material structure.
2. Description of the Related Art
Interferometric profilometry enables the performance of non-contact measurements of surfaces with high resolution and at high measurement speeds. Accordingly, several widely accepted techniques have been developed in the art for calculating surface topography from optical interference data recovered from two conventional approaches, namely phase-shifting interferometry (PSI) and vertical-scanning interferometry (VSI).
Phase-shifting interferometry is based on changing the phase difference between two coherent interfering beams using narrow-band light or a single wavelength, λ, in some known manner, for example by changing the optical path difference (OPD) either continuously or discretely with time. Several measurements of light intensity with different OPD values, usually equally spaced, at a pixel of a photodetector can be used to determine the phase difference between the interfering beams at the point on a test surface corresponding to that pixel. Based on such measurements at all pixels with coordinates (x,y), a phase map Φ(x,y) of the test surface can be obtained, from which very accurate data about the surface profile may be calculated using well known algorithms.
PSI provides a vertical resolution on the order of better than 1/100 of a wavelength; thus, it is well suited for characterizing smooth, well-reflecting surfaces. At the same time, the PSI technique has a limited vertical range of application because of the so-called 2π ambiguity; i.e., the fact that the phase shift between two beams is repeated with 2π periods every time the OPD exceeds a distance of λ/2. This “phase wrapping” behavior of PSI leads to ambiguity in the measurements of the surface profile when the surface features are higher than λ/2. Thus, in practice, conventional PSI techniques have been limited to measurements of fairly smooth and continuous surfaces because only in such cases can phase-unwrapping algorithms be applied to reconstruct the surface shape.
Large-step, rough, or steep-surface measurements, on the other hand, have been traditionally carried out with white-light (or broadband-light) vertical-scanning interferometry. As conventionally implemented, VSI uses a white-light source and the reference arm of the interferometer is scanned vertically with respect to a stationary test sample (or vice versa). The degree of contrast of fringes produced on the detector by two interfering beams (instead of their phases) is measured as a function of distance between the reference and test surfaces to obtain information about the test surface. The contrast of a VSI interferogram is maximum when the OPD approaches zero and the test surface topography may be reconstructed by determining the peak position of the modulation envelope of the interferogram for each detector pixel. The VSI approach overcomes the limited scanning range associated with PSI techniques, but suffers from significantly lower resolution (about 3 nm) and, therefore, is not as precise as PSI.
Together, PSI and VSI make it possible to measure most samples. However, both are based on having a uniform reflectivity at each region of the sample surface corresponding to each detector pixel. (For convenience, the term pixel is used hereinafter to refer both to a detector pixel and to the corresponding region of the sample surface.)
Multi-material structures, hereinafter referred to as “composite” materials or structures, are necessarily characterized by an optically non-homogeneous surface because of the different optical properties of the materials. In particular, the phase change on reflection (typically referred to as “PCOR” in the art) used for the interferometric measurement of a composite structure may vary from point to point on the test surface depending on the particular composition of the material illuminated by the test beam. When two or more materials are present in a sample pixel, the resulting PCOR is an undefined combination of the PCORs generated by all materials within that pixel and detected at the corresponding detector pixel.
Furthermore, composite structures are typically also characterized by irregular surfaces because of the granularity produced by the interfaces between materials. This structural characteristic is found to be present even when the surface is highly polished. As a result, the single height produced by the interferometric measurement at a given pixel is necessarily incorrect because of the nano-scale non-planar structure of the test surface. Therefore, the interferometric surface characterization of test samples made of dissimilar materials has been problematic.
The problem is particularly significant with regard to the manufacture of read/write magnetic-head sliders, where precise and rapid profilometry is essential for quality control purposes. The precise height of the various slider components is critical to ensure performance and long product life. As illustrated schematically in the top view and cross-section of FIGS. 1(A) and 1(B), respectively, magnetic-head sliders include an air-bearing surface 10 (ABS) made of an aluminum-oxide/titanium-carbide composite material (often referred to as AlTiC), a read/write pole-tip region 12, and a trailing edge surface 14 made of aluminum oxide. The working distance between the air bearing surface of the slider and the disk surface affects the potential for a mechanical crash as the head flies over the disk. Similarly, the distance between the pole tip and the disk affects signal loss during read/write operations.
Therefore, standard tests carried out for quality control during manufacture of head sliders involve the measurement of the difference between the heights of the ABS surface 10 and the trailing edge surface 14 (commonly referred to as the aluminum oxide trailing-edge recession, or ALR, parameter) and of the distance between the heights of the ABS surface 10 and the pole tip 12 (commonly referred to as the pole tip recession, or PTR, parameter). The composite ABS surface 10 is precision polished in order to render it as flat as possible for optimal functionality. Thus, the height of the ABS surface is conveniently identified for the purpose of calculating the ALR and PTR parameters by fitting a plane surface 16 to the height data obtained by means of an interferometric measurement of a predetermined ABS region. However, for the reasons mentioned above, the composite structure and the corresponding granularity of the AltiC material tend to produce imprecise height measurements by conventional interferometry.
Various approaches have been used in the art to overcome this shortcoming of interferometry. For example, one approach has been to determine global refraction indices (n,k) for the ABS region using ellipsometry and to establishes a linear relationship between n and the reflectance R of the ABS surface. A well-known formula relating PCOR to n and R is then used to calculate a single overall PCOR value for the ABS surface, which can be used to correct the inteferometric measurement. See K. H. Womack et al., “IEEE Transactions on Magnetics,” Vol. 34, No. 2, March 1998, p. 459.
Another approach is based on the assumption that the effective complex reflectivity, rmix, for a mixture of two materials [of composition ε % TiC and (1−ε) % Al2O3] is given by the linear relationship rmix=εrTiC+(1−ε)rAl2O3. Thus, a theoretical value for rmix is simply calculated on the basis of known quantities (ε, rTiC, and rAl2O3). Global refraction indices (n,k) are then generated by ellipsometry and used in an empirical equation to calculate a global PCOR for the ABS region as a function of the assumed effective complex reflectivity and the measured global refraction indices. See Peter de Groot, “Applied Optics,” Vol. 37, No. 28, October 1998, p. 6654.
Still another approach is disclosed by Mansfield et al. in U.S. Patent Publication No. 2006/0176522. These authors use an empirical formula for calculating a height correction for the ABS region as a function of the average modulation amplitude over the trailing-edge surface, the local modulation amplitude at the pixel of interest, and several parameters determined empirically. Specifically, one parameter is related to the instrument and is calculated by comparing results obtained from known surfaces; another parameter is calculated so as to minimize roughness from a known set of height data; and two more parameters are selected for numerical and normalization purposes.
None of these methods achieves the degree of accuracy desired for the interferometric measurement of ALR and PTR parameters of magnetic-head sliders. For quality-control purposes, it would be very desirable to achieve an accuracy of about 1 nm RMS or better, but current techniques can do no better than about 3-4 nm RMS. This invention provides a further advance in the art based on a pixel-by-pixel analysis of the composition of the multi-material ABS surface and a calculation of a local correction factor for each pixel height generated by interferometry.